Answer:
x = 35°
Step-by-step explanation:
These are corresponding angles. When a transversal crosses 2 parallel lines, 4 angles are created at each intersection, and each pair of corresponding angles between those are congruent.
These angles are congruent, so you can set them equal to each other:
Then, just solve for x:
You can check that by plugging it back into both:
Answer:
A. 31/100
Step-by-step explanation:
Change 3/10 to hundreds:
3/10 × 10/10 = 30/100
The denominator (the bottom number) must be 100.
61 - 30 is 31.
The missing number is 31/100. See image.
You labeled the triangle wrong sides 'a' and 'b' are supposed to be the sides that make the right angle. the other side is called the hypotenuse which is the longest side which you should have labeled 'c'
so Pythagorean theorem says
a^2+b^2=c^2
so
(2x+1)^2+(11x+5)^2=(12x+1)^2
distribute
(4x^2+4x+1)+(121x^2+110x+25)=(144x^2+24x+1)
add like terms
125x^2+114x+26=144x^2+24x+1
subtract 125x^2 from both sides
114x+26=19x^2+24x+1
subtract 114x from both sides
26=19x^2-90x+1
subtract 26 from both sides
0=19x^2-90-25
factor
(x-5)(19x+5)=0
therefor x-5=0 and/or 19x+5=0
so
x-5=0 add 5 to both sides
x=5
19x+5=0
subtract 5 from both sides
19x=-5
divide both sides by 19
x=-5/19
since side legnths can't be negative, we can cross this solution out
so x=5
subtitute
1+2x
1+2(5)
1+10=11
side a=11
11x+5
11(5)+5
55+5=60
side b=60
12x+1
12(5)+1
60+1=60
side c=61
add them all up
side a+b+c=11+60+61=132=total legnth
Here is some thoughts on this:
cos 57 = sin (90-57) = sin 33
so cos 57 . cosec 33 = cos 57 / sin 33 = sin 33 / sin33 = 1
2 cos 60 = 2 * 1/2 = 1
so the last 2 parts work out to 0
now we have to find cos 70 / sin 20
sin 20 = cos 70 so this comes to 1
so finally the answer is 1
